 So maybe we passed to Marco. I saw Marco showing up and probably you saw the sunset or at least you are muted at least here. Okay, so Marco, yes. And so Marco, can you share the screen? Yes. So I should be sharing right now. This is my presentation. And this is the first slide. Very good. Screen. Yes, yes, perfect. So okay, so you can go ahead. You have 20 minutes. Okay, thank you. And thank you for inviting me, especially Lice. Too bad we're not all in Trieste now, but okay, at least we can see the sunset. So what I'm going to talk about, so we are a group of essentially theoretical physicists. And we do a lot of modeling. A lot of it is data driven. But what I'm going to talk about today is more like a conceptual model of gene sweeps. And so there will be no data in this talk. It's a very simple thing. But, you know, there is one message that I think is related to a lot of things that were raised in previous talks. Unfortunately, I'm teaching this week heavy duty, so I missed a lot of talks. Some of it I saw and it was very interesting. And I'm trying to catch up a little bit by looking at the videos. Anyway, if I can change my slide, first of all, I want to acknowledge who worked on this project. Basically, the idea came up with some discussions a few years ago with Joshua Weitz and then Jacopo Grilli, who's there at ICTP, implemented the first version of the model. And then Simone is basically now bringing home this study and trying to conclude it. We are writing it up right now. So any feedback actually is useful. So basically, I'm going to tell you three things. And the first thing is that bacteria share genes as an introduction. But this is completely obvious, I think, to this audience. So I'm just going to use some work we did on gene families to reiterate this concept that was raised by, I think, most of the talks of this workshop. This is just a network of horizontal transfers of gene families that you see between a bunch of bacteria to see that there's a lot. And what we did is a model for gene family exchange, a simple, neutral, collisional model, looking at the abundance profiles of gene families. For example, in the data, you can quantify them by PFAMs. How many PFAMs of one PFAM family you find in bacteria. And you can do the statistics of abundance across bacteria and look at the fluctuations of abundance. And the model predicts that basically the more horizontal you need horizontal transfers to have some dispersion in these family abundance. And if you have like gene family expansions, you have even more dispersion. But in the data, you also see this kind of blue histograms of specific gene families where you have under dispersed compared to what the model prediction family. So the prediction is that these families do not do any horizontal transfer. And this is basically what you see looking at horizontal transfers quantified by standard phylogenetic methods, that you have a relation between the dispersion of family abundance and the amount of horizontal transfers. This means that basically a genome is both fluid and stable, depending on the functional content that you look at. So if you look at the right functional contact, it's stable and it's vertically inherited. And it's a phylogenetic tree. Whereas if you look at other kinds of functional contact, for example, all the families that you find on plasmids, the genome is very fluid, but not only those, the genome, even, you know, metabolic enzymes are transferred a lot. The genome is very fluid. And there is no real phylogeny, but you find more like a network. So it's both a tree and a network. So this was my introduction, but what I really want to talk about is not that genes are shared a lot, but also that genes sweep. And we will clarify in a minute what it means that they sweep. So they don't sweep your kitchen, but they sweep your microbial communities. And we were inspired by this study that appeared now 10 years ago in science whereby methods of basically comparative genomics, they discovered in planton a few genes that were clearly beneficial in some sets of vibrio strains that spread without reducing the diversity of the community. So somehow these genes were beneficial. They were spreading, but then across species, across strains. So the question is, how is that possible? Because, you know, if you think about this problem with the simple paradigm of population genetics, you would expect that the first guy that gets this beneficial gene gets an advantage, a higher fitness, and will spread in the population with its own genome. You will get a genome sweep, not a gene sweep. So how can you spread a beneficial gene in a community with many species across many species, more or less preserving the diversity of that community? That's the conceptual problem that they raised at the end of that paper. Basically, they had a few propositions. Their main proposition, which is not really a mathematical model, so we're going to try to support our idea with a mathematical model, was that, okay, maybe you have very fast horizontal gene transfer rates, and then you have, quickly after, you have differentiation of different ecotypes. So now there's a barrier and this guy, the gene has spread, and these guys, they cannot basically do genome sweeps on each other. That was their idea originally. And they also proposed towards the end of the paper that, okay, okay, maybe there's some frequency dependent selection due to different deleterious genes, for example, genes that are under phages, that are linked with the beneficial gene. And this idea that they was proposed originally by Shapiro as a concept was built by Kunihiko Kaneko and Takeuchi in several papers. This was the first one into a mathematical model where they show that, yeah, indeed, this is possible. But this model requires that every time this beneficial gene is linked with a different deleterious gene, which is possible, but so far, maybe not systematically the case, and so far there's no experimental validation of this, but certainly it's a possibility. Another study proposed that maybe if the horizontal gene transfer rates and the migration rates are very fast, you can also have a single population where the gene can spread in more than one species. But I think if you look at the numbers, you have really to push a lot on the numbers to get this diversity within a single population. So this is so far the debate on this, as far as I know, maybe simplifying a little bit on possible explanations of these gene sweeps. And we have another proposition, and that's the last part of what I'm going to talk about, which is not mutually exclusive with the ones that I presented you, but it's another mechanism that could work on top of those. And our idea is that metapopulation structure, so the structure of a community divided in sub-communities islands, where you have migration and different populations in each island, could actually help preserving the diversity in a gene sweep. And this is something that we built into a conceptual model. So if you want to visualize for plankton, for example, what could be, what could give the structure of a metapopulation, it's basically marine snow. And this applies to the Shapiro data. Basically, this Vibrio, they live on chitin fragments that are found in the ocean. And each fragment can host several species and supplies the nutrients. And then you can have migration from these fragments. It's really a metapopulation structure. Other microbial communities, for example, the gut, it's not that clear what the metapopulation structure could be, but it's a complex and way community. So it's possible that the same could apply to other kinds of communities. But to be honest, we didn't really think about it very seriously. So this is our model. Actually, this is a little bit of a premise. In order to formulate the question of how a beneficial gene introduced by horizontal transfer and genome sweep could affect the diversity of a community, you have to supply a model for the diversity of a community. But the results that I discussed don't really depend on which model you supply. To fix the ideas, we basically used this neutral model of biodiversity, which, if you are familiar with population genetics, is equivalent to the infinite alleles model, except that the alleles are the islands. So these circles are islands, they are populations. And then you can have different species, the colors on an island. And you have introduction of a new species with some probability and migration with removal of an existing species on an island with some other, as a complementary move. And this gives you some stable diversity. And that's the only thing, for example, that we will need. That there is a stable diversity and that your model for diversity is kind of homeostatic. So if you change the diversity, it will tend to go back to the diversity with some time scale. The real model that we did is about the gene sweep. So now you have your species on the islands. And as you can see, these islands have only one color. So we work in the hypothesis that the rates of migration and horizontal transfer are not high enough to supply multiple species on a single subpopulation. And the zeros and the ones are the presence of the beneficial gene. So I have a genome sweep with migration move with some probability in the model where basically I get another one, but with the same color of the previous one. So this is a genome sweep. But then I get a horizontal transfer move. So a gene sweep kind of move where the ones can spread without changing the color. So in this case, this is the same, the gene has moved to the other island on a different species and it has swept within that species. Okay. So what happens when you run this very simple model? You start from population with steady diversity. These are different realizations of assimilation. And then here you introduce the new beneficial gene and then you get some reduction. Of course, because you have these moves, these kind of moves, you get a reduction in the diversity. But this reduction is not a reduction to zero. That's the whole point. So you get some kind of reduction which depends on your parameters. And you can quantify your reduction by the ratio of the final to the initial diversity. And you can take average values of this because you can have variabilities from realization to realization. So basically, you only have one parameter, one relevant parameter, which is the relative rate of horizontal transfer to sweep, this pH over PM. And you want to quantify how much diversity you have left, depending on this new, which sets the initial diversity, basically. That's the initial biodiversity model. So if you have no horizontal transfer, of course, you end up with zero diversity. But any value, even small, will preserve, let's say, even 50% with the ratio of 0.1, you already have 50% of the diversity of the initial diversity of the population. And then if you have a homeostatic diversity, it could increase again. So this doesn't really depend on the parameter. The other nice thing about this model, but this is not super relevant here, is that it's so simple that you can do analytical calculations, and then you get a match with your simulations. And this is just to reiterate the message with different parameters. You get still a good agreement. You get a good agreement between the predicted values for this ratio from simulation theory. And then you have the last thing that I'm going to tell you, which is the timescale separation or timescale overlap issue. So you have a timescale, which you can see here, by which you reduce your diversity when you introduce a beneficial gene in your metapopulation in our model. And then here you have a slower timescale, which here basically is in this plot. You don't see it, but you're going to see it in a second, where you may have a sort of recovery to the equilibrium value of the diversity, which depends on the mechanisms that preserve diversity in your community. So far, I showed you the model basically under an assumption that these timescales are very separated, but these timescales can have some overlap. And of course, you can run the model with considering these overlaps. So in this case, you have a quick loss of diversity due to the introduction of the beneficial gene spreading across species. And then you have a slower recovery due to the homeostatic mechanisms within your community. In our case, a neutral model that preserve biodiversity. You can run the model with multiple rounds of beneficial sweeping genes. In this case, here, here, and here. And then if basically the prediction is that if you don't get a beneficial gene every day, basically your community will get some kind of stable diversity. But anyway, it's the other conceptual contribution. It's a matter of timescales. So how much and how fast does your gene sweep decrease your diversity? And how fast does your community recover its diversity? Okay, and this is just the same thing. So only if you have very frequent sweeps, do you reduce on a long-term basis the average diversity of your community. So again, it's very, very simple, maybe too simple. But the advantage is that with such a simple model, it's also very clear what the ingredients do. That's it. I'm done. So basically, we have this metapopulation hypothesis supported by this very simple model. And our idea is that it's not contrary to other things that have been proposed, but it could play a role. So the next thing would be to try to support it with data. This is not super simple, but it's not impossible, I think. That would be our next project, which has not started yet. So thank you for your attention. Thank you, Marco. Thank you very much. So maybe we can have some, if there are some questions for the talk of Marco. Can I make a comment more than a question? Yes. So I might be wrong because it's late and it's been a bumpy day again. But it seems to me that you are kind of showing a model of how plasmids, how conegative plasmids are maintained in a population in between strains. Yes. Well, I didn't know anything about plasmids. You didn't mean to, but it seems, no, because in this case, we have data. There are people around. Yes. I mean, I think this model, if there are plasmid data on like the ones that there were two three talks yesterday on plasmid spreading within microbial communities. And I think I mean, we had it in mind. We developed this model with this plankton idea in mind. And in this Shapiro paper, they don't really know the mechanism. And I don't know if by now people have worked on the mechanisms of like whether, for example, these genes are carried by plasmids. Typically they didn't say and they didn't know. But I also think that what there was one mathematical model presented yesterday about the spread of where Mike broke us. Yes. And in that model, diversity was not irrelevant variable, but they looked at stability. And that's why I asked, you know, that diversity, did you look at diversity and they say, he said, yeah, we can look at diversity and we know that it's reduced. That's what I would expect, that there is a reduction. And then it would be interesting to see whether there is a recovery. What are the mechanisms? So again, might be relevant. We just didn't think about it before